Kepler's area law in the Principia: filling in some details in Newton's proof of Proposition 1

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• 作者：Nauenberg ; Michael
• 关键词：01A45 ; Kepler's area law ; Newton's Principia
• 刊名：Historia Mathematica
• 出版年：2003
• 出版时间：November, 2003
• 年：2003
• 卷：30
• 期：4
• 页码：441-456
• 全文大小：166 K

文摘

During the past 30 years there has been controversy regarding the adequacy of Newton's proof of Prop. 1 in Book 1 of the Principia. This proposition is of central importance because its proof of Kepler's area law allowed Newton to introduce a geometric measure for time to solve problems in orbital dynamics in the Principia. It is shown here that the critics of Prop. 1 have misunderstood Newton's continuum limit argument by neglecting to consider the justification for this limit which he gave in Lemma 3. We clarify the proof of Prop. 1 by filling in some details left out by Newton which show that his proof of this proposition was adequate and well-grounded.